Binary and Bases: Lesson
Lesson 1 of 1
  1. 1
    We use number bases every day without realizing it. When we think about numbers in everyday life, we are almost always thinking of decimal numbers, or numbers in base 10, where each digit of a numb…
  2. 2
    While we as humans intuitively use decimal base in our everyday lives, there are other base systems that are very important to mathematics and computers. For example, binary, base 2, is the underly…
  3. 3
    Now that we’ve discussed how a binary number is represented, as well as some important reasons we use binary numbers, we know wonder how computers can convert binary numbers to information we can t…
  4. 4
    Another method we can use to convert numbers from one base to another is using what is known as the division method. In the division method, we divide a decimal number by the value of the base as m…
  5. 5
    Any number can be a base; however, only a few are common on computers. The ones we discussed previously (hexadecimal, decimal, octal, and binary) are the most common on computer systems. Octal num…
  6. 6
    We can convert octal to decimal in the same way we converted binary to decimal. For example, we use the powers of eight just as we did in the lookup table to convert 0o456 to decimal: | power | …
  7. 7
    We convert decimal to octal in the same way we convert decimal to binary. We can use the division method with the root of 8 and reverse the numbers at the end. We start with the decimal number and …
  8. 8
    Hexadecimal (base 16), often called “hex,” is a convenient and concise way to represent binary numbers on a computer. Hex numbers are often used for values like colors and any other place where we …
  9. 9
    We can convert hexadecimal to decimal in a similar way we converted binary to decimal, using the powers method. As a reminder, hexadecimal digits have 16 possible values, 0-9 and a-f. A famous h…
  10. 10
    We use the same division technique for octal and binary to convert decimal to hexadecimal, except we divide using 16. We will use decimal 112 again. | Division by 16 | Remainder | Hex | | ——…

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